Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 1 
Assessment:  EX 100% 
Supplementary Assessment:  MA40125 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:  Before taking this unit you must take MA20225 
Description:  Aims & Learning Objectives: Aims: To study further Markov processes in both discrete and continuous time. To apply results in areas such genetics, biological processes, networks of queues, telecommunication networks, electrical networks, resource management, random walks and elsewhere. Objectives: On completing the course, students should be able to * Formulate appropriate Markovian models for a variety of real life problems and apply suitable theoretical results to obtain solutions * Classify a variety of birthdeath processes as explosive or nonexplosive * Find the Qmatrix of a timereversed chain and make effective use of time reversal. Content: Topics covering both discrete and continuous time Markov chains will be chosen from: Genetics, the WrightFisher and Moran models. Epidemics. Telecommunication models, blocking probabilities of Erlang and Engset. Models of interference in communication networks, the ALOHA model. Series of M/M/s queues. Open and closed migration processes. Explosions. Birthdeath processes. Branching processes. Resource management. Electrical networks. Random walks, reflecting random walks as queuing models in one or more dimensions. The strong Markov property. The Poisson process in time and space. Other applications. 
Programme availability: 
MA40125 is Optional on the following programmes:Department of Mathematical Sciences
